Chronic disease management often involves sequential decisions that have long-term implications. Those decisions are based on high dimensional information, which pose a problem for traditional modeling paradigms. In some key instances, the disease dynamics might not be known, but instead are learned as new information becomes available. As a first step, we will describe some of the ongoing research modeling medical decisions of patients with chronic conditions. Key to the models developed is the incorporation of the individual patient's disease dynamics into the parameterization of the models of the disease state evolution. Model conception and validation is described, as well as the role of multidisciplinary collaborations in ensuring practical impact of this work.
A group of scientists at the University of North Carolina, from theorists to clinicians, have coalesced over the past decade on an effort called the Virtual Lung Project. There is a parallel VLP at the Pacific Northwest Laboratory, focused on environmental health, but I will focus on our effort. We come from mathematics, chemistry, computer science, physics, lung biology, biophysics and medicine. The goal is to engineer lung health through combined experimental-theoretical-computational tools to measure, assess, and predict lung function and dysfunction. Now one might ask, with all due respect to Tina Turner: what's math got to do with it? My lecture is devoted to many responses, including some progress yet more open problems.
Infectious diseases continue to have a major impact on individuals, populations, and the economy, even though some of them have been eradicated (e.g. small pox). Unlike many other ecological systems, many infectious diseases are well documented by spatio-temporal data sets of occurrence and impact. In addition, in particular for childhood diseases, the dynamics of the disease in a single individual are fairly well understood and fairly simple. As such, infectious diseases are a great field for mathematical modeling, and for connecting these models to data. In this article, we concentrate on three issues, namely (1) comparative childhood disease dynamics and vaccination, (2) spatio-temporal disease dynamics, and (3) evolution in diseases with multiple strains. The mathematical techniques used in the analysis of disease models contain bifurcation theory for ODEs, wavelet analysis, stochastic simulations and various forms of data fitting.